The patterned assembly and stepwise Vps4-mediated disassembly of composite ESCRT-III polymers drives archaeal cell division

ESCRT-III family proteins form composite polymers that deform and cut membrane tubes in the context of a wide range of cell biological processes across the tree of life. In reconstituted systems, sequential changes in the composition of ESCRT-III polymers induced by the AAA–adenosine triphosphatase Vps4 have been shown to remodel membranes. However, it is not known how composite ESCRT-III polymers are organized and remodeled in space and time in a cellular context. Taking advantage of the relative simplicity of the ESCRT-III–dependent division system in Sulfolobus acidocaldarius, one of the closest experimentally tractable prokaryotic relatives of eukaryotes, we use super-resolution microscopy, electron microscopy, and computational modeling to show how CdvB/CdvB1/CdvB2 proteins form a precisely patterned composite ESCRT-III division ring, which undergoes stepwise Vps4-dependent disassembly and contracts to cut cells into two. These observations lead us to suggest sequential changes in a patterned composite polymer as a general mechanism of ESCRT-III–dependent membrane remodeling.


Computational details
The ESCRT-III filaments were initialized as five short polymers placed successively along the inner surface of a long, tubular, deformable membrane (Fig. 5A). To model the filaments, we used the ESCRT-III model we developed in Harker-Kirschneck 2019 (19), in which the filament consists of three beaded monomers that are bonded to their neighbouring monomers via nine harmonic bonds. The bond strength determines the stiffness of the polymer, whereas the exact ratio of the bond lengths give the filament its chiral curvature. The filament can constrict or expand its target radius by modifying its bond lengths.
Here each filament consisted of 1.05 helical loops (82 monomers). Two filament recruitment patterns were investigated as the initial configuration of the molecular dynamics (MD) simulations: CdvB1-CdvB2-CdvB-CdvB2-CdvB1 (termed "CdvB1 out"), CdvB2-CdvB1-CdvB-CdvB1-CdvB2 (termed "CdvB1 in"). The target radii of CdvB (purple), CdvB2 (cyan), CdvB1 (yellow) were set as = 17 , 2 = 4.0 , �/2 (i.e., 1 = 6.5 ), where is the MD unit of length and corresponds to roughly 10 nm. Filament bond stiffness was set as = 2 = 250 / 2 , 1 = 50 / 2 . CdvB1 was given a tilt 1 = 40 ∘ , and we investigated whether the outward (< >) or inward (> <) conical direction at filament recruitment had an impact on the filament separation and constriction. The membrane was modelled with the one-particle-thick model developed by Yuan 2010 (59). The membrane tube consisted of 5000 beads and had an initial radius of = 18 . The tube length in x direction along the simulation box was set to = 360 . The size of the coarsegrained beads was = = 0.5 . Short-ranged 12-6 Lennard-Jones (LJ) interactions were applied between the two bottom beads of the filament's three-beaded subunits and the membrane beads: The interaction strength was set to = 3.0 and the cut-off distance to = 1.3 ⋅ , where = 2 1 6 is the inter-particle contact distance and Ec is the energy at cut-off distance.
Volume exclusions was applied between different filament subunits and between the membrane and the top beads of the filament. The volume exclusion interactions were treated as LJ interactions truncated at rmin and shifted to zero, with the interaction strength set as to volex = 2.0 . Periodic boundary conditions were applied in three dimensions. We performed molecular dynamics simulations using the molecular dynamics package LAMMPS (60) and integrated the equations of motion with a timestep 0.01 0, where t0 is the MD unit of time, coupled to a Langevin thermostat. The Langevin thermostat was applied at every step with the temperature set to 1 and the damping coefficient set to 1 0. The box size and the number of particles were initially kept constant. Initially the system was equilibrated for t=100 0, with all three filament types having the same target radius RCdvB = RCdvB1 = RCdvB2 = 17 . This allowed the membrane to attach to the filament loops from the outside. Then CdvB remained at = 17 , while CdvB1 and CdvB2 reduced their target radius to RCdvB1 = 6.5 and CdvB2 to RCdvB2 = 4.0 respectively. We then let the system to evolve for = 2×10 5 0, until the formation of a stable filament distribution formed. In Vps4+ simulations, we disassembled the CdvB filament by severing its internal bonds and turned the interaction between bottom beads and membrane beads from attractive interactions to pure volume exclusion immediately after the initial equilibration. We carried out ten independent simulations for each setup and the configurations of the last snapshots of the trajectories were used to calculate the normalized filament density (Fig. 5A, S6A-S6B). We visualize our simulation results using To see if this newly found filament alignment (CdvB1-CdvB2-CdvB1 with CdvB1 tilted inwards) can cause cells to divide, we placed two opposing CdvB1 filaments (each three loops long) around a single looped CdvB2 filament inside a membrane tube with Rtube = 27 . In this simulation filament curvature is changed progressively, by picking random monomers within the filament and constricting them, instead of releasing all the filament energy at once (Fig.   S7A). As shown in Harker-Kirschneck et al. 2022 with a single filament, this dynamical protocol led to the most reliable and symmetric division and came remarkably close to matching the kinetics of ring constriction measured from experimental data (35). In this new simulation setup with multiple ESCRT-III filaments, the cubical simulation box had a length of 400 and CdvB1 was given a large tilt 1 = 90 ∘ . The large tilt allowed CdvB1 to decrease the diameter of the membrane neck by providing a surface for the membrane to glide over and into the neck.
The filament stiffness was set to 1 = 2 = 400 / 2 . After equilibrating the membrane on its own for 200 0 , we started transitioning the CdvB1 filaments at random positions from the initial state ( 1 = , 1 = 0°) to its tilted and constricted final state Every 100 simulation steps one subunit in each CdvB1 filament got transformed, while the CdvB2 filament remained in its initial state ( 2 = ).
Then the CdvB2 filament in the middle was transitioned by transforming one random subunit within the filament from a large to a small target radius every 10000 steps, until the entire filament was transitioned. This transition was much slower, as the target radius of CdvB2 has to decrease dramatically from 2 = to 2 = 1.75 -by about 93.5%. After constriction was completed, we disassembled the filaments by severing the bonds between random subunits within the filament -first CdvB1 and then CdvB2, which led to division. We found that scission only occurs reliably if i) the target radius is very small, Rtarget ≤ 2σ, and ii) we use the ensemble that preserves the constant zero pressure along the axis of the simulation box, instead of preserving the volume of the box. This maintains the membrane under low tension by allowing the membrane area to shrink/increase as needed (by adjusting the simulation box size). This supports the finding of Lafaurie 2013, who show that membrane tubes under tension do not divide (61).
When simulating filament separation, we initially placed the filaments on the membrane as three interlaced strands, consisting of two full helical loops (Fig. S5A). Each filament strand was modelled by our three-bead-monomer ESCRT-III model (19) and consisted of 156 monomers. The membrane tube consisted of 30000 beads. The initial radius of the membrane tube was = 18 , with length in x direction = 216 . Initially the system was equilibrated for t = 100 0 with CdvB, CdvB1 and CdvB2 all at the same target radius = 1 = 2 = 17 , to ensure that all three filaments attached to the interior of the membrane tube. We then activated CdvB1 and CdvB2 by resetting their target radii, and allowed the system to evolve until the filaments were fully separated (typically 10 5 to 10 6 0 ).           Table S3. List of primary antibodies, host animal and supplier.
Movie S2. Live cell imaging of S. acidocaldarius expressing CdvB2ΔMIM2, displaying rigid membrane protrusions.
Movie S3. Coarse-grained molecular dynamics simulations of Vps4+ conditions described in